Geodesic
Free Algebras of Automorphic Forms on the Upper Half-Plane
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 81-89

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We find all pairs $(\Gamma,a)$ consisting of a cocompact Fuchsian group $\Gamma$ of genus zero and an automorphy factor $a$ of $\Gamma$ for which the graded algebra of $a$-$\Gamma$-automorphic forms is free.
Keywords: Fuchsian group, cocycle, automorphic form, free algebra. 
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     author = {O. V. Schwarzman},
     title = {Free {Algebras} of {Automorphic} {Forms} on the {Upper} {Half-Plane}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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O. V. Schwarzman. Free Algebras of Automorphic Forms on the Upper Half-Plane. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 81-89. http://geodesic.mathdoc.fr/item/FAA_2003_37_2_a8/